Sits

If we’re trying to think about sits, we need to know the budget, average lead cost, and the number of leads it takes to get a sit.

For the first, let’s say we spend $400 per day in the phoenix area, and $100 per day in Nevada, and let’s assume that people in Nevada are indistinguishable from people in AZ. It’s probably not true that people from both groups are fungible, but I have no data on NV, so I don’t have anything else to work with. So that would be $500*30 to get $15000 for November. It’s already the 1st and we’re not doing any VN spend yet but let’s just keep things simple.

For the latter pair of variables, there is unfortunately quite a bit of uncertainty. We’re running new ads, and we’re also making changes to the appointment setting department, and we don’t know what the effects of these changes will be. But we can consider ranges of possibilities.

To get a range of plausible values for the number of leads it takes to get a sit, we can use past data. We can use data from April 1st to September 30th to get a sense of things.

We usually talk about the number of leads it takes to get a sit. But to be able to do anything interesting with stats and probability it would be useful to convert that rate into a proportion. So if it takes 10 leads to get one sit, that’s the same as .1 of 10 leads turning into a sit. This proportion can then be thought of as a probability. In this case it’s the probability of a lead turning into a sit.

Since probabilities can range from 0 to 1, what we’d like to know is how likely all these values from 0 to 1 are, so we can see which is most likely, and get a range of plausible values to work with. We can then convert those back into our familiar rate (number of leads needed to get one sit)

A common approach for estimating this uses Bayes theorem. If we use it, we get:

Along the x-axis are possible values of the probability we’re interested in (likelihood a lead turns into a sit). The y-axis is density. It’s best not to try and make too much sense of density visually, but the gist of it is that greater the density (area under the curve), the more likely its associated x-axis value is. We want to know a range of plausible values, and one common way of defining that is to say we’re going to find densest interval that contains say 95% of the area under the curve (Area under the curve represents probability, and so sums to 1). If we do that we get 0.0640641 and 0.1091091 (indicated by green and blue dashed lines). If we convert those back into rates, we get 16 and 9 (rounded). So we could use these as a range of plausible values for our stat of interest, which is the number of leads it takes to get a sit. The most likely value converts to 12 (red dashed line), which you also could have found by just dividing the total number of leads by the number of sits: 568/48 ~= 12.

So now that we have a range of plausible values for the number of leads it takes to get a sit, and we know our budget, we can consider some different scenarios.

The reddish line represents the average number of sits expected, given our budget, and a lead per sit ratio of 12, for a range of average lead costs. This is the line most consistent with our actual performance from April thru September. If we at least don’t get worse, then we’d expect something like that, on average. So say if leads are $125 (average cost in October) on average in November, we’d hope for approximately 10 sits. Of course there could be variability over any sample, but that’s the value we’d expect on average, if the future continues to be like the past.

The calculation for any point on the line is just the budget divided by the average lead cost, to get the number of leads, and then you divide that by the number of leads needed to get one sit. For the value in the previous paragraph, it’s 15000/125, to get 120 leads. Then 120/12 to get 10 sits.

The blue and green lines should be interpreted as corresponding to the upper and lower limits for the plausibility for how many leads it takes to get one sit (ironically the blue line is the lower, and the green is the upper. look at the chart legend). So they are not particularly likely, but rather are like cutoffs between plausibility and implausibility (again, this is somewhat arbitrary. We’ve selected an interval of possible values for the statistic that is highly consistent with our data, which is bracketed by these two values)

If the appointment setting department were to do better than usual, we’d move towards the blue line. At the same average lead cost, we’d then expect approximately 13 sits on average, if we got all the way to the blue line. You can explore other possibilities by hovering your cursor over the line, as the data viz is interactive.

These sits should not be expected to all happen in November. Some would probably happen later.

Reasons for skepticism

If we put a bunch of energy into trying to get the appt setting department (or whatever we’re calling it) humming, then maybe we can at least not do worse than usual in the short term, and can do better than our past performance in the medium and long term